We use the spinor-helicity method [1]} to describe
the external graviton states of amplitudes (for reviews see Refs. [2]}).
The natural quantities in this formalism are two component Weyl spinors
\((\lambda _i)_\alpha \equiv [u_+(k_i)]_\alpha \,, \hspace{36.98866pt}(\tilde{\lambda }_i)_\alpha \equiv [u_-(k_i)]_\alpha \,,\) 
